In spite of those impressive characteristics, the Tu-22 has three major flaws which would likely consign it to become a second Sovremenny-class white elephant.
First, the Tu-22 is highly, highly vulnerable to interception, and it and the Tu-160 are the planes around which the USN has designed its entire anti-air suite. From a strategic standpoint, it's not really worth it to buy the capability your intended adversary has already spent billions building defenses against.
Second, the Tu-22 is not guaranteed to link well with the tightly linked, 21st-century, C4ISR model that the PLAN/PLAAF want to have. This could turn it into a one-off albatross that looks great on paper but is a pain in the ass for field commanders to use.
Third, the Tu-22 will be expensive and will dilute PLAAF defense budgets away from areas which they really should be focusing on, like UCAVs, 5th-gen avionics, AWACS, and better engines.
Finally, the capability the Tu-22 provides--1500 mi unrefuelled combat radius at supersonic speeds with 50 tons of standoff ordnance--can be done with a flight of J-20s. But that flight of J-20s has three main advantages over a Tu-22:
1) Survivability -- the J-20 is a stealth airframe with radar-reduction and much better maneuverability. It will be much better at punching through an F/A-18 CAP than a Tu-22M3 would.
2) Versatility -- those same J-20s that fly out on a shipping hunt can be re-armed for air superiority missions on the next sortie. The Tu-22 can't.
3) Infinitely better C4ISR -- the J-20 can link with home base, friendly AWACS, and surface ships in a much better fashion than the Tu-22 thanks to its indigenous software systems.
In many ways, the fact that CAC is building the J-20 means China doesn't need the Backfire. Now, the Blackjack, with its 8000 mile range, is another story, but I highly, highly, highly doubt Russia would ever sell one of them.
